The average annual growth rate in Net Sales for the industry from 1995 onwards was 20

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If the average cost of a privately owned vehicle, is one-third of income per capita, how much would the entire population of Zone C have spent on privately owned vehicles in total (to the nearest Billion €’s)?

Efficiency is the Operating Cash Flow as a percentage of total costs (Goods Sold & Fixed Costs). What was the efficiency of IPG in 1996?

Can you find the next number to replace the “?” for the following sequences? Hint: there will be a underlying rule to find the next numbers – think outside the box!

1. 7, 12, 18, 25, ? 2. 3, 10, 21, 36, ?

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The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It doesn't take compounding into account.

Average annual growth rate (AAGR) is the average annualized return of an investment, portfolio, asset, or cash flow over time.
AAGR is calculated by taking the simple arithmetic mean of a series of returns.
AAGR is a linear measure that does not account for the effects of compounding—to account for compounding, compound annual growth rate (CAGR) would be used instead.

$\begin{aligned} &AAGR = \frac{GR_A + GR_B + \dotso + GR_n}{N} \\ &\textbf{where:}\\ &GR_A=\text{Growth rate in period A}\\ &GR_B=\text{Growth rate in period B}\\ &GR_n=\text{Growth rate in period }n\\ &N=\text{Number of payments}\\ \end{aligned}$

The average annual growth rate helps determine long-term trends. It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed. The ratio tells you your average annual return.

The average annual growth rate is a calculation of the arithmetic mean of a series of growth rates. AAGR can be calculated for any investment, but it will not include any measure of the investment's overall risk, as measured by its price volatility. Furthermore, the AAGR does not account for periodic compounding.

AAGR is a standard for measuring average returns of investments over several time periods on an annualized basis. You'll find this figure on brokerage statements and in a mutual fund's prospectus. It is essentially the simple average of a series of periodic return growth rates.

One thing to keep in mind is that the periods used should all be of equal length—for instance, years, months, or weeks—and not to mix periods of different duration.

The AAGR measures the average rate of return or growth over a series of equally spaced time periods. As an example, assume an investment has the following values over the course of four years:

Beginning value = $100,000
End of year 1 value = $120,000
End of year 2 value = $135,000
End of year 3 value = $160,000
End of year 4 value = $200,000

The formula to determine the percentage growth for each year is:

$\text{Simple percentage growth or return} = \frac{\text{ending value}}{\text{beginning value}} - 1$

Thus, the growth rates for each of the years are as follows:

Year 1 growth = $120,000 / $100,000 - 1 = 20%
Year 2 growth = $135,000 / $120,000 - 1 = 12.5%
Year 3 growth = $160,000 / $135,000 - 1 = 18.5%
Year 4 growth = $200,000 / $160,000 - 1 = 25%

The AAGR is calculated as the sum of each year's growth rate divided by the number of years:

$\frac{20 \% + 12.5 \% + 18.5 \% + 25 \%}{4} = 19\%$

In financial and accounting settings, the beginning and ending prices are usually used. Some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed.

As another example, consider the five-year real gross domestic product (GDP) growth for the United States over the last five years. The U.S. real GDP growth rates for 2017 through 2021 were 2.3%, 2.9%, 2.3%, -3.4%, and 5.7%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 1.96%, or (2.3% + 2.9% + 2.3% + -3.4% + 5.7%) / 5.

AAGR is a linear measure that does not account for the effects of compounding. The above example shows that the investment grew an average of 19% per year. The average annual growth rate is useful for showing trends; however, it can be misleading to analysts because it does not accurately depict changing financials. In some instances, it can overestimate the growth of an investment.

For example, consider an end-of-year value for year 5 of $100,000 for the AAGR example above. The percentage growth rate for year 5 is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year 1 and the ending value of year 5, the performance yields a 0% return. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR).

The CAGR smooths out an investment's returns or diminishes the effect of the volatility of periodic returns.

$\frac{\text{Ending Balance}}{\text{Beginning Balance}}^{\frac{1}{\text{\# Years}}} - 1$

Using the above example for years 1 through 4, the CAGR equals:

$\frac{\$200,000}{\$100,000}^{\frac{1}{4}}- 1 = 18.92\%$

For the first four years, the AAGR and CAGR are close to one another. However, if year 5 were to be factored into the CAGR equation (-50%), the result would end up being 0%, which sharply contrasts the result from the AAGR of 5.2%.

Because AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk involved in the investment, as calculated by the volatility of its price. For instance, if a portfolio grows by a net of 15% one year and 25% in the next year, the average annual growth rate would be calculated to be 20%.

To this end, the fluctuations occurring in the investment’s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement.

A second issue is that as a simple average it does not care about the timing of returns. For instance, in our example above, a stark 50% decline in year 5 only has a modest impact on total average annual growth. However, timing is important, and so CAGR may be more useful in understanding how time-chained rates of growth matter.

The average annual growth rate (AAGR) identifies long-term trends of such financial measures as cash flows or investment returns. AAGR tells you what the annual return has been (on average), but it does not take into account compounding.

AAGR may overestimate the growth rate if there are both positive and negative returns. It also does not include any measure of the risk involved, such as price volatility—nor does it factor in the timing of returns.

Average annual growth rate (AAGR) is the average increase. It is a linear measure and does not take into account compounding. Meanwhile, the compound annual growth rate (CAGR) does and it smooths out an investment's returns, diminishing the effect of return volatility.

The average annual growth rate (AAGR) is calculated by finding the arithmetic mean of a series of growth rates.